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The 8th Wonder of the World: Compound Interest
Albert Einstein is famously quoted as saying, "Compound interest is the eighth wonder of the world. He who understands it, earns it... he who doesn't, pays it." Unlike simple interest, which is linear and predictable, compound interest is exponential. It is the financial force that turns small, consistent habits into massive wealth over time. This calculator helps you harness that power.
The Secret Used by Banks
The magic variable is n (Frequency). The more often you compound, the faster P grows. This is why banks love to pay you annual interest but charge you daily interest on credit cards.
The Snowball Effect Explained
Year 1
Invest $100 at 10%.
+$10 Profit
Year 2
Invest $110 at 10%.
+$11 Profit (You made $1 extra!)
"That extra $1 doesn't seem like much, but over 30 years, that extra layer of interest on interest is what turns $10,000 into $174,000."
Frequency Matters (On $10,000 at 10%)
| Compounding | Times Per Year (n) | Final Amount (1 Yr) |
|---|---|---|
| Annually | 1 | $11,000.00 |
| Quarterly | 4 | $11,038.13 |
| Monthly | 12 | $11,047.13 |
| Daily | 365 | $11,051.56 |
Quick Trick: The Rule of 72
Divide 72 by your interest rate to know when your money doubles.
72 ÷ 8% = 9 Years to double your money.
72 ÷ 12% = 6 Years to double your money.
Frequently Asked Questions
What is Compound Interest?
Compound interest is "interest on interest". Unlike simple interest which only grows on the principal, compound interest allows your interest payments to start earning their own interest. This creates a snowball effect that accelerates wealth growth over time.
What is the Compound Interest formula?
The formula is A = P(1 + r/n)^(nt). A = Final Amount, P = Principal, r = Annual Interest Rate (decimal), n = Number of times interest is compounded per year, t = Number of years.
How does compounding frequency affect my return?
The more frequently interest is compounded (added to your account), the faster your money grows. Daily compounding yields slightly more than monthly, which yields more than annual compounding.
What is the Rule of 72?
The Rule of 72 is a quick mental math trick to estimate how long it takes to double your investment. Divide 72 by your interest rate. Example: At 9% return, money doubles in 8 years (72 ÷ 9 = 8).
What is the difference between APR and APY?
APR (Annual Percentage Rate) is the simple interest rate stated by the bank. APY (Annual Percentage Yield) is the actual return you earn after factoring in compounding. APY is always higher than or equal to APR.
How does time impact compound interest?
Time is the most powerful variable. Due to exponential growth, starting 10 years earlier can often result in having double or triple the wealth at retirement, even if you invest less money overall.
Does inflation eat away compound interest?
Yes. To calculate your "Real Rate of Return", you must subtract the inflation rate from your investment return. If you earn 8% but inflation is 3%, your real purchasing power only grows by 5%.
Why is credit card debt so dangerous?
Credit cards use compound interest against you. They typically compound daily with high rates (20%+). This allows small balances to balloon into massive debts very quickly if minimum payments are missed.
What investments offer compound interest?
Savings accounts, CDs, and Bonds pay explicit interest. Stocks and Real Estate provide returns through "Compounded Annual Growth Rate" (CAGR) via reinvested dividends and asset appreciation.
Can I lose money with compound interest?
In a savings account, no (it is guaranteed). But in the stock market, negative compounding (losses) can hurt your portfolio. A 50% loss requires a 100% gain just to get back to even.
Should I reinvest my dividends?
Yes! Reinvesting dividends is the key to compounding in the stock market. It buys you more shares, which then pay more dividends, creating a powerful feedback loop.
How much do I need to retire?
A common rule of thumb is the "4% Rule". You generally need 25 times your annual expenses invested. This calculator helps you see if your current savings rate will get you there.